Dozens of people who have custody of their grandchildren will soon be moving into a Bronx apartment complex, thanks to an affordable housing project that’s the first of its kind in the country.

Mayor Bloomberg dropped by the building yesterday to present 75-year-old Dorothy Jenkins with a gift – a welcome mat for her new three-bedroom apartment on Prospect Avenue that she’ll soon share with her two grandchildren.

Jenkins, who raised four children of her own, took custody of her grandson, 19, and her granddaughter, 12, after her daughter died when she was just 32.

She will pay about $300 a month, which includes on-site counseling, after-school programs and 24-hour security.

“Everything is going to be better,” said Jenkins, who currently lives in a small two-bedroom apartment in a housing project.

“I have to share a bedroom with my granddaughter, and she’s getting very upset about that. Twelve-year-old girls don’t want to share a bedroom with their grandmother.”

Dubbed “The Grandparent Apartments,” the six-story building has 40 two-bedroom apartments and 10 three-bedroom apartments. Families are expected to begin moving in within the next few weeks.

The $12 million cost is being paid with city, state and private funds.

Officials estimate that there are 100,000 households in the city with custody of grandchildren.